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Fill in the first difference and the second difference for the following patterns - Junior Cycle Mathematics - Question 9 - 2014
Question 9
Fill in the first difference and the second difference for the following patterns. Some of Pattern 1 has been completed for you. Pattern 1: 2 4 9 17 28 Fi... show full transcript
Worked Solution & Example Answer:Fill in the first difference and the second difference for the following patterns - Junior Cycle Mathematics - Question 9 - 2014
Step 1
First difference: (Change)
Answer
To calculate the first difference for Pattern 1, we find the differences between consecutive terms:
- 4 - 2 = 2
- 9 - 4 = 5
- 17 - 9 = 8
- 28 - 17 = 11
The completed first difference for Pattern 1 is therefore: 2, 5, 8, 11.
For Pattern 2, the first difference is:
- 2 - (-1) = 3
- 5 - 2 = 3
- 8 - 5 = 3
- 11 - 8 = 3
The completed first difference for Pattern 2 is: 3, 3, 3, 3.
Step 2
Second difference: (Change of change)
Answer
For Pattern 1, the first differences are 2, 5, 8, 11. The second difference is found by calculating the differences between the first differences:
- 5 - 2 = 3
- 8 - 5 = 3
- 11 - 8 = 3
The second difference is constant, which is 3 for all.
For Pattern 2, the first differences are all 3, so the second difference is:
- 3 - 3 = 0
- 3 - 3 = 0
- 3 - 3 = 0
Thus, the second difference for Pattern 2 is 0.
Step 3
State whether each pattern is linear or quadratic.
Answer
For Pattern 1:
- It is quadratic. The reason is that the first differences change, and the second difference is constant, which indicates a quadratic relationship.
For Pattern 2:
- It is linear. The reason is that the first difference is constant, which indicates a linear relationship.